Topic 2 - 2 Dimensional Arrays

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Topic 2 - 2 Dimensional Arrays
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2D Arrays in Java

• Arrays with multiple dimensions may be declared
  and used
• int mat new int34
• the number of pairs of square brackets indicates
  the dimension of the array.
• could have an array of 3 dimensions, or 4 or
  more, but AP only covers arrays of 1 or 2
  dimensions

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Number of Rows and Columns

• Once 2D array created access elements with 2
  subscripts
• int mat new int34
• by convention, in a 2D array the first subscript
  indicates the row number and the second the
  column number
• mat has 3 rows and 4 columns per row

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Coordinates of a Cell

• When accessing elements 2 subscripts are needed
• the first subscript indicates the row
• the second subscript indicates the column
• int mat new int34
• mat23 12

column
row
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2 Dimensional Arrays
row
0 1 2 3
column
0 1 2
0 0 0 0 0 0 0 0 0 0 0
0
This is our abstract picture of the 2D array
mat21 12
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The Real Picture
0 1 2 3
0 0 0 0
0 1 2
0 1 2 3
0 0 0 0
mat
0 1 2 3
0 0 0 0
mat holds the memory address of an array with
3 elements. Each element holds the memory
address of an array of 4 ints
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Arrays of Multiple Dimension

• because multiple dimensional arrays are treated
  as arrays of arrays of arraysmultiple
  dimensional arrays can be ragged
• each row does not have to have the same number of
  columns
• each row array has its own length variable
• this is rarely used and is not tested on APCS

int raggedMat new int5for(int i 0
i lt raggedMat.length i) raggedMati new
inti 1
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Rectangular 2D Arrays

• Ragged arrays are sometime useful, but normally
  we deal with rectangular 2D arrays
• each row has the same number of columns as every
  other row
• use this a lot as precondition to methods that
  work on matrices
• given int mat
• mat.length refers to the number of rows in the 2D
  array
• mat0.length refers to the number of columns per
  row

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Working with 2D Arrays

• It is very common to have to access all elements
  of a 2D array
• Simplest way to do this is with a nested for loop.

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Example of nested for Loops

• String temp
• for(int i 0 i lt 4 i) for(int j 0 j lt
  3 j) temp "" i "," j " "
• System.out.print( temp )
• System.out.println()
• What is the output?

outer loop
inner loop
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Output of Example

• 0,0 0,1 0,2
• 1,0 1,1 1,2
• 2,0 2,1 2,2
• 3,0 3,1 3,2
• What would out be if the println statement were
  removed?

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2D Array Example

• Find the maximum value in a 2D array of ints
• must search every element
• public int findMax(int mat) / pre mat !
  null, mat.length gt 0, mat0.length gt 0,
  mat is rectangular
• post return maximum element in mat
• /

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findMax Implemented
public int findMax(int mat) int max
mat00 for(int r 0 r lt mat.length
r) for(int c 0 c lt mat0.length
c) if( matrc gt max ) max
matrc return max
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Conway' Game of Life

• A more complicated 2D Array problem
• Conway's Game of Life www.math.com/students/wonder
  s/life/life.html
• cells are either occupied by an organism or empty
• next generation depends on the current status
  (occupied or empty) and your 8 neighboring cells
• occupied cell
• 0 - 1 neighbors, organism dies (loneliness)
• 2 - 3 neighbors, organism lives
• gt 4 neighbors, organism dies (over crowding)
• empty cell
• 3 neighbors birth, organism born

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Game of Life Example
"" -gt occupied, "." -gt empty, generation 0
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Game of Life
added number of neighboring cells that are
occupied
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Game of Life
apply all changes simultaneously, generation 1
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Game of Life
apply all changes simultaneously, generation 2
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Game of Life
apply all changes simultaneously, generation 3
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Game of Life
apply all changes simultaneously, generation 4
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Game of Life
apply all changes simultaneously, generation 5
(and so forth)
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Game of Life nextGen method

• Write a method that returns a 2D array of
  booleans that represents the next generation
  based on the current generation
• public boolean nextGen(boolean
  world) / pre world ! null, mat.length gt 0,
  mat0.length gt 0, world is
  rectangular
• post return next generation of world
  based on rules of Game of Life
• /

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nextGen source code
public boolean nextGen(int world)
final int ROWS world.length final int COLS
world0.length boolean result new
booleanROWSCOLS int num for(int r
0 r lt ROWS r) for(int c 0 c lt
COLS c) num getNumNeighbors(worl
d, r, c) //check for alive and
survives if( worldrowcol ( num
2 num 3)
resultrowcol true // check for
birth else if( !worldrowcol
num 3) resultrowcol
true
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2D Array in the MBCS

• The AP Marine Biology Case Study uses a 2D array
  in its BoundedEnv class
• the BoundedEnv class represents an area of water
  in which the fish in the MBCS are located
• instance variables for BoundedEnv
• private Locatable theGrid
• private int objectCount

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the allObjects method

• a method in the BoundedEnv class
• returns an array with a reference to everything
  in the BoundedEnv
• typical 2D array processing (nested loop)
• makes use of helper methods instead of accessing
  length variables directly (numRows, numCols)

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the allObjects source code
/ pre none Returns all the
objects in this environment. _at_return an
array of all the environment objects /
public Locatable allObjects()
Locatable theObjects new LocatablenumObjects(
) int tempObjectCount 0   //
Look at all grid locations. for ( int r
0 r lt numRows() r ) for ( int c
0 c lt numCols() c ) // If
there's an object at this location, // put it
in the array. Locatable obj
theGridrc
if ( obj ! null )
theObjectstempObjectCount obj
tempObjectCount
return theObjects